Trabalho Estatistica
Equipe:
Carlos Alberto Figueiredo - RM330568
Daiana Cristina Zanelli Mota - RM330722
Diogo Silva Rocha - RM330717
Renato Belandrino Rodrigues - RM330579
install.packages(“psych”) install.packages(“plotly”) install.packages(“gmodels”) install.packages(“corrgram”) install.packages(“lmtest”) install.packages(“rpart”) install.packages(“rpart.plot”) install.packages(“RandomForest”)
# mostrar atÈ 2 casas decimais
options("scipen" = 2)
# Ler arquivo csv
Vinhos <- read.csv2("BaseWineRedeWhite2018.csv", row.names=1)#Vinhos <- BaseWine_Red_e_White2018
#fix(Vinhos)
#mostrar as vari·veis
str(Vinhos)## 'data.frame': 6497 obs. of 13 variables:
## $ fixedacidity : num 6.6 6.7 10.6 5.4 6.7 6.8 6.6 7.2 5.1 6.2 ...
## $ volatileacidity : num 0.24 0.34 0.31 0.18 0.3 0.5 0.61 0.66 0.26 0.22 ...
## $ citricacid : num 0.35 0.43 0.49 0.24 0.44 0.11 0 0.33 0.33 0.2 ...
## $ residualsugar : num 7.7 1.6 2.2 4.8 18.8 ...
## $ chlorides : num 0.031 0.041 0.063 0.041 0.057 0.075 0.069 0.068 0.027 0.035 ...
## $ freesulfurdioxide : num 36 29 18 30 65 16 4 34 46 58 ...
## $ totalsulfurdioxide: num 135 114 40 113 224 49 8 102 113 184 ...
## $ density : num 0.994 0.99 0.998 0.994 1 ...
## $ pH : num 3.19 3.23 3.14 3.42 3.11 3.36 3.33 3.27 3.35 3.11 ...
## $ sulphates : num 0.37 0.44 0.51 0.4 0.53 0.79 0.37 0.78 0.43 0.53 ...
## $ alcohol : num 10.5 12.6 9.8 9.4 9.1 9.5 10.4 12.8 11.4 9 ...
## $ quality : int 5 6 6 6 5 5 4 6 7 6 ...
## $ Vinho : Factor w/ 2 levels "RED","WHITE": 2 2 1 2 2 1 1 1 2 2 ...#mostra as vari·veis
names(Vinhos)## [1] "fixedacidity" "volatileacidity" "citricacid"
## [4] "residualsugar" "chlorides" "freesulfurdioxide"
## [7] "totalsulfurdioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
## [13] "Vinho"#XX Variáveis e muita informaçãoattach(Vinhos)
# FrequÍncia absoluta
table(as.factor(Vinhos$quality), Vinhos$Vinho, useNA = "ifany")##
## RED WHITE
## 3 10 20
## 4 53 163
## 5 681 1457
## 6 638 2198
## 7 199 880
## 8 18 175
## 9 0 5table(as.factor(Vinhos$quality), Vinhos$Vinho)##
## RED WHITE
## 3 10 20
## 4 53 163
## 5 681 1457
## 6 638 2198
## 7 199 880
## 8 18 175
## 9 0 5Análise:
Avaliando as duas tabelas de frequência das notas/qualiade que comparam os vinhos tintos e brancos, vemos que não exsitem valores “brancos/NA” já que as duas tabelas apresentam as mesmas frequências.
Olhando os valores entre as duas tabelas, testamos a hipótese da resposta de qualidade ser diverente entre os vinhos Brancos e Tintos. Para isso fizemos um Teste para duas amostras
Quality <- split(Vinhos, Vinhos$Vinho)
t.test(Quality$WHITE$quality, Quality$RED$quality)##
## Welch Two Sample t-test
##
## data: Quality$WHITE$quality and Quality$RED$quality
## t = 10.149, df = 2950.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.1951564 0.2886173
## sample estimates:
## mean of x mean of y
## 5.877909 5.636023Análise:
A partir do valor do p-value e risco alfa máximo de 5%, podemos dizer que os vinhos Brancos e Tintos tem valores médios de notas diferentes, já que o p-value < 2.2e-16
# 2-Way Cross Tabulation
library(gmodels)## Warning: package 'gmodels' was built under R version 3.4.4CrossTable(as.factor(Vinhos$quality), Vinhos$Vinho) ##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 6497
##
##
## | Vinhos$Vinho
## as.factor(Vinhos$quality) | RED | WHITE | Row Total |
## --------------------------|-----------|-----------|-----------|
## 3 | 10 | 20 | 30 |
## | 0.927 | 0.303 | |
## | 0.333 | 0.667 | 0.005 |
## | 0.006 | 0.004 | |
## | 0.002 | 0.003 | |
## --------------------------|-----------|-----------|-----------|
## 4 | 53 | 163 | 216 |
## | 0.000 | 0.000 | |
## | 0.245 | 0.755 | 0.033 |
## | 0.033 | 0.033 | |
## | 0.008 | 0.025 | |
## --------------------------|-----------|-----------|-----------|
## 5 | 681 | 1457 | 2138 |
## | 45.546 | 14.869 | |
## | 0.319 | 0.681 | 0.329 |
## | 0.426 | 0.297 | |
## | 0.105 | 0.224 | |
## --------------------------|-----------|-----------|-----------|
## 6 | 638 | 2198 | 2836 |
## | 5.154 | 1.683 | |
## | 0.225 | 0.775 | 0.437 |
## | 0.399 | 0.449 | |
## | 0.098 | 0.338 | |
## --------------------------|-----------|-----------|-----------|
## 7 | 199 | 880 | 1079 |
## | 16.681 | 5.446 | |
## | 0.184 | 0.816 | 0.166 |
## | 0.124 | 0.180 | |
## | 0.031 | 0.135 | |
## --------------------------|-----------|-----------|-----------|
## 8 | 18 | 175 | 193 |
## | 18.321 | 5.981 | |
## | 0.093 | 0.907 | 0.030 |
## | 0.011 | 0.036 | |
## | 0.003 | 0.027 | |
## --------------------------|-----------|-----------|-----------|
## 9 | 0 | 5 | 5 |
## | 1.231 | 0.402 | |
## | 0.000 | 1.000 | 0.001 |
## | 0.000 | 0.001 | |
## | 0.000 | 0.001 | |
## --------------------------|-----------|-----------|-----------|
## Column Total | 1599 | 4898 | 6497 |
## | 0.246 | 0.754 | |
## --------------------------|-----------|-----------|-----------|
##
## Análise:
A partir da tabela cruzada entre tipo do vinho (Branco e Tinto) e as notas de qualidade, podemos perceber a maior frequencia geral é de notas 6 (43,7%).
Mas olhando para cada tipo de vinho individualmente, a nota 6 é mais frequente para o vinho branco(44,9%), enquanto a nota mais frenquente para o vinho tinto é 5 (42,6%), o que ajuda a confirmar a diferença entre os vinhos, com relação as notas de qualidade.
summary(Vinhos)## fixedacidity volatileacidity citricacid residualsugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.60
## 1st Qu.: 6.400 1st Qu.:0.2300 1st Qu.:0.2500 1st Qu.: 1.80
## Median : 7.000 Median :0.2900 Median :0.3100 Median : 3.00
## Mean : 7.215 Mean :0.3397 Mean :0.3186 Mean : 5.44
## 3rd Qu.: 7.700 3rd Qu.:0.4000 3rd Qu.:0.3900 3rd Qu.: 8.10
## Max. :15.900 Max. :1.5800 Max. :1.6600 Max. :45.80
## chlorides freesulfurdioxide totalsulfurdioxide density
## Min. :0.00900 Min. : 1.00 Min. : 6.0 Min. :0.9871
## 1st Qu.:0.03800 1st Qu.: 17.00 1st Qu.: 77.0 1st Qu.:0.9923
## Median :0.04700 Median : 29.00 Median :118.0 Median :0.9949
## Mean :0.05603 Mean : 30.53 Mean :115.7 Mean :0.9947
## 3rd Qu.:0.06500 3rd Qu.: 41.00 3rd Qu.:156.0 3rd Qu.:0.9970
## Max. :0.61100 Max. :289.00 Max. :440.0 Max. :1.0140
## pH sulphates alcohol quality
## Min. :2.720 Min. :0.2200 Min. : 0.9567 Min. :3.000
## 1st Qu.:3.110 1st Qu.:0.4300 1st Qu.: 9.5000 1st Qu.:5.000
## Median :3.210 Median :0.5100 Median :10.3000 Median :6.000
## Mean :3.219 Mean :0.5313 Mean :10.4862 Mean :5.818
## 3rd Qu.:3.320 3rd Qu.:0.6000 3rd Qu.:11.3000 3rd Qu.:6.000
## Max. :4.010 Max. :2.0000 Max. :14.9000 Max. :9.000
## Vinho
## RED :1599
## WHITE:4898
##
##
##
## Análise:
Olhando as estatísticas básicas de todas as proprieddes, podemos perceber alguns pontos:
Médias próximas as medianas, que indica possível simetria nas distribuições para: fixedacidity, volatileacidity, citricacid, chlorides, freesulfurdioxide, totalsulfurdioxide, density, pH, sulphates, alcohol e quality.
Avaliando os valores máximos e mínimos, temos indícios de outliers para: citricacid (mínimo e máximo), residualsugar (máximo), chloride (máximo), freesulfurdioxide (máximo), sulphates (máximo).
aggregate (Vinhos,
by = list(Vinho),
FUN = "mean")## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA## Group.1 fixedacidity volatileacidity citricacid residualsugar chlorides
## 1 RED 8.319637 0.5278205 0.2709756 2.538806 0.08746654
## 2 WHITE 6.854788 0.2782411 0.3341915 6.387332 0.04577236
## freesulfurdioxide totalsulfurdioxide density pH sulphates
## 1 15.87492 46.46779 0.9967467 3.311113 0.6581488
## 2 35.30808 138.36066 0.9940223 3.188267 0.4898469
## alcohol quality Vinho
## 1 10.40008 5.636023 NA
## 2 10.51427 5.877909 NAAnálise:
Função retorna a media de todas as vaiáveis numéricas para os vinhos Brancos e Tintos Pontos que chamam a atenção:
residualsugar é muito maior para os brancos apesar do alcohol ter valores próximos.
freesulfurdioxide e totalsulfurdioxide é maior nos vinhos brancos que nos tintos. Este conservante também serve para previnir o escurecimento dos vinhos. Por isso, talvez, sua maior concentração nos Brancos.
O cometário “argument is not numeric or logical: returning NAargument is not numeric or logical: returning NA” é devido a variável vinho que não é numérica
mean(Vinhos$fixedacidity) # mÈdia## [1] 7.215307median(Vinhos$fixedacidity) # mÈdiana## [1] 7quantile(Vinhos$fixedacidity,type=4) # Quartis## 0% 25% 50% 75% 100%
## 3.8 6.4 7.0 7.7 15.9quantile(Vinhos$fixedacidity,.65,type=4) # exato percentil## 65%
## 7.3range(Vinhos$fixedacidity) # amplitude## [1] 3.8 15.9diff(range(Vinhos$fixedacidity)) #diferenÁa entre o maior e o menor valor## [1] 12.1min(Vinhos$fixedacidity) # valor mÌnimo de x## [1] 3.8max(Vinhos$fixedacidity) # valor m·ximo de x## [1] 15.9var(Vinhos$fixedacidity) # para obter a vari‚ncia## [1] 1.68074sd(Vinhos$fixedacidity) # para obter o desvio padr„o## [1] 1.296434CV_fixedacidity<-sd(Vinhos$fixedacidity)/mean(Vinhos$fixedacidity)*100 # para obter o coefiiente de variaÁ„o
CV_fixedacidity## [1] 17.96783Análise:
As funções retornam estaísticas decritivas para a variavel fixedacidity, inclusive o Coeficiente de Variação (CV).
CV = Em teoria das probabilidades e estatística, o coeficiente de variação (CV), também conhecido como desvio padrão relativo (DPR), é uma medida padronizada de dispersão de uma distribuição de probabilidade ou de uma distribuição de frequências. É frequentemente expresso como uma porcentagem, sendo definido como a razão do desvio padrão pela média (ou seu valor absoluto. O CV ou DPR é amplamente usado em química analítica para expressar a precisão e a repetitividade de um ensaio. Também é comumente usado em campos como engenharia e física quando se fazem estudos de garantia de qualidade e avaliações de repetitividade e reprodutibilidade. O CV também é usado por economistas e investidores em modelos econômicos e na determinação da volatilidade de um valor mobiliário. Fonte: Wikipédia
#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
hist(fixedacidity)
hist(volatileacidity)
hist(citricacid )
hist(residualsugar)
hist(chlorides)
hist(freesulfurdioxide)
hist(totalsulfurdioxide)
hist(density)
hist(pH)
hist(sulphates)
hist(alcohol)
hist(quality)
Análise:
Avaliando os histogrmas, alguns pontos chamam a atenção:
As escalas estão bem abertas, indicando a presença de Outliers, principalmente para: volatileacidity, citricacid, chlorides, freesulfurdioxide
Distribuições assimetricas, com mínimos limitados pelo valor zero, por exemplo: volatileacidity, residualsugar, chlorides, freesulfurdioxide
hist(quality, col=c("pink"), col.main="darkgray", prob=T)
Análise:
- O histograma da quality, por ter valores inteiros, o histograma parece “dentado” mas que não invalida a análise de uma distribuição simétrica, possivelmente Normal
attach(Vinhos)## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(Vinhos$quality, main='quality')
Análise:
As análises dos Box Plots validam as que já fizemos para os histogramas.
Apesar de todos os Box Plots apresentarem Outliers, que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide. citricacid, freesulfurdioxide e alcohol com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.
Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.
boxplot(quality ~ Vinho, main='quality')
boxplot(fixedacidity ~ Vinho, main='fixedacidity',col=c('red','blue'))
boxplot(volatileacidity ~ Vinho , main='volatileacidity')
boxplot(citricacid ~ Vinho, main='citricacid')
boxplot(residualsugar ~ Vinho, main='residualsugar',col=c('red','blue'))
boxplot(chlorides ~ Vinho, main='chlorides')
boxplot(freesulfurdioxide ~ Vinho, main='freesulfurdioxide')
boxplot(totalsulfurdioxide ~ Vinho, main='totalsulfurdioxide')
boxplot(density ~ Vinho, main='density')
boxplot(pH ~ Vinho, main='pH')
boxplot(sulphates ~ Vinho, main='sulphates')
boxplot(alcohol ~ Vinho, main='alcohol')
Análise:
Os Box Plots para todas as características, agora comparando os vinhos brancos e tintos podem servir para entender características que podem distinguir entre estes dois tipos e vinhos, como já fizemos com a quality, usando o teste de hipótese.
Olhando os Box Plots, outras características que podem ser diferentes por tipo de vinho são: volatileacidity, chlorides, freesulfurdioxide e totalsulfurdioxide (já comentado nas estatísticas descritivas)
# Gr·fico de dispers„o ( pch=caracter, lwd=largura)
plot(freesulfurdioxide~totalsulfurdioxide)
plot(freesulfurdioxide~totalsulfurdioxide, pch=1, lwd=3)
plot(freesulfurdioxide~totalsulfurdioxide)
abline(h=mean(freesulfurdioxide), col="red")
abline(v=mean(totalsulfurdioxide), col="green")
Análise:
O Gráfico de dispersão mostra a relação de previsão entre as variáveis. Neste caso entre freesulfurdioxide e totalsulfurdioxide.
Estas variáveis aparentam ter uma correlação forte (núvem de pontos com pouca dispersão) e positiva (inclinação positiva/coeficiente angular > 0), indicando que a partir da informação sobre totalsulfurdioxide pode prever o valor de freesulfurdioxide, com boa acuracidade.
A linha verde representa a média do totalsulfurdioxide e a vermelha a média do freesulfurdioxide. O ponto onde onde as retas se encontram é um dos pontos que fará parte da regressão linear entre as variáveis e da uma ideia de centramento desta relação
attach(Vinhos)## The following objects are masked from Vinhos (pos = 3):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidityVinhos$fx_redSugar <- cut(residualsugar,breaks=c(0,10,20,30,max(residualsugar)))
Vinhos$fx_redSugar ## [1] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [7] (0,10] (0,10] (0,10] (20,30] (0,10] (0,10]
## [13] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [19] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [25] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [31] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [37] (0,10] (0,10] (0,10] (10,20] (10,20] (20,30]
## [43] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [49] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [55] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [61] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [67] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [73] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [79] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [85] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [91] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [97] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [103] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [109] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [115] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [121] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [127] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [133] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [139] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [145] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [151] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [157] (10,20] (10,20] (0,10] (10,20] (10,20] (0,10]
## [163] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [169] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [175] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [181] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [187] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [193] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [199] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [205] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [211] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [217] (10,20] (0,10] (0,10] (20,30] (10,20] (10,20]
## [223] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [229] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [235] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [241] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [247] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [253] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [259] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [271] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [277] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [283] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [289] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [295] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [301] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [307] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [313] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [319] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [325] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [331] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [337] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [343] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [349] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [355] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [361] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [367] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [373] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [379] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [385] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [391] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [397] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [403] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [409] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [415] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [421] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [427] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [433] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [439] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [445] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [451] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [457] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [463] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [469] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [475] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [487] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [493] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [499] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [505] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [511] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [517] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [523] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [529] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [535] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [541] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [547] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [553] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [559] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [565] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [571] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [577] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [583] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [589] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [595] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [601] (0,10] (0,10] (20,30] (10,20] (0,10] (0,10]
## [607] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [613] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [619] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [625] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [631] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [637] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [643] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [649] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [655] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [661] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [667] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [673] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [679] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [685] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [691] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [697] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [703] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [709] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [715] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [721] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [727] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [733] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [739] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [745] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [751] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [757] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [763] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [769] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [775] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [781] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [787] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [793] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [799] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [805] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [811] (0,10] (10,20] (10,20] (0,10] (10,20] (10,20]
## [817] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [823] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [829] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [835] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [841] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [847] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [853] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [859] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [865] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [871] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [877] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [883] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [889] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [895] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [901] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [907] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [913] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [919] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [925] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [931] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [937] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [943] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [949] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [955] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [961] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [967] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [973] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [979] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [985] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [991] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [997] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1003] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1009] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1015] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1021] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1027] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1033] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1039] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1045] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1051] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1057] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1063] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1069] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1075] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1081] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1087] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1093] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1099] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1105] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [1111] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1117] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1123] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1129] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1135] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1141] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1147] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1153] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1159] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1165] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1171] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1177] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1183] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1189] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1195] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1201] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1207] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [1213] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1219] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [1225] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1231] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1237] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [1243] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1249] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1255] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1261] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1267] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1273] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1279] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1285] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1291] (0,10] (0,10] (0,10] (10,20] (10,20] (10,20]
## [1297] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1303] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1309] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1315] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [1321] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1327] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1333] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1339] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1345] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1351] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1357] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1363] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1369] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1375] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1381] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1387] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1393] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1399] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1405] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1411] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1417] (0,10] (10,20] (0,10] (0,10] (0,10] (20,30]
## [1423] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1429] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1435] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1441] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1447] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1453] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1459] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1465] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1471] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1477] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1483] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1489] (0,10] (10,20] (20,30] (0,10] (0,10] (0,10]
## [1495] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1501] (0,10] (0,10] (10,20] (0,10] (30,45.8] (0,10]
## [1507] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1513] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1519] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1525] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1531] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1537] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1543] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1549] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [1555] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1561] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1567] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1573] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1579] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1585] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1591] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1597] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1603] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1609] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1615] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1621] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1627] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1633] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1639] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1645] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1651] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1657] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1663] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1669] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1675] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [1681] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1687] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1693] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1699] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1705] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1711] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1717] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1723] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1729] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1735] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1741] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1747] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1753] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1759] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1765] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1771] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1777] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1783] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [1789] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1795] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1801] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1807] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1813] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1819] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1825] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [1831] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1837] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1843] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [1849] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1855] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1861] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1867] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1873] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1879] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1885] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1891] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1897] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1903] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1909] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [1915] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1921] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1927] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1933] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1939] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1945] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1951] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1957] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1963] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1969] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1975] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1981] (0,10] (0,10] (0,10] (0,10] (0,10] (20,30]
## [1987] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [1993] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1999] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2005] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2011] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2017] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2023] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2029] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2035] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2041] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2047] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2053] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2059] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2065] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2071] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2077] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2083] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2089] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2095] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2101] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2107] (10,20] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2113] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2119] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2125] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2131] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2137] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2143] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2149] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2155] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2161] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2167] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2173] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [2179] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2185] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2191] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2197] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2203] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2209] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2215] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2221] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2227] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2233] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2239] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2245] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2251] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2257] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2263] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [2269] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2275] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2281] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2287] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2293] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2299] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2305] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2311] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2317] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2323] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2329] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2335] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [2341] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2347] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2353] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2359] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2365] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2371] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2377] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2383] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [2389] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2395] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2401] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2407] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2413] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2419] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2425] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2431] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2437] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2443] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2449] (10,20] (10,20] (0,10] (10,20] (10,20] (0,10]
## [2455] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2461] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2467] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [2473] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2479] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2485] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2491] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2497] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2503] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2509] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2515] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2521] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2527] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2533] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2539] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2545] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2551] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2557] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2563] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2569] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2575] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2581] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2587] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2593] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2599] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2605] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2611] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2617] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2623] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [2629] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [2635] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2641] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2647] (0,10] (20,30] (0,10] (0,10] (0,10] (0,10]
## [2653] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2659] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2665] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2671] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2677] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2683] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2689] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2695] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2701] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2707] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2713] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2719] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2725] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2731] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2737] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2743] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2749] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2755] (10,20] (10,20] (10,20] (10,20] (0,10] (0,10]
## [2761] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2767] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2773] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [2779] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2785] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2791] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2797] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2803] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2809] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2815] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2821] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2827] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2833] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2839] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2845] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2851] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2857] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2863] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2869] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2875] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2881] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2887] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2893] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2899] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2905] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2911] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2917] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2923] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2929] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2935] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2941] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2947] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2953] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2959] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2965] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2971] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2977] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2983] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2989] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2995] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3001] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3007] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3013] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3019] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3025] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3031] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3037] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3043] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3049] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3055] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3061] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3067] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3073] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3079] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3085] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3091] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3097] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3103] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3109] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3115] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3121] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3127] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3133] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3139] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3145] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3151] (0,10] (0,10] (0,10] (0,10] (0,10] (20,30]
## [3157] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3163] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3169] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3175] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3181] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3187] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3193] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3199] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3205] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3211] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3217] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3223] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3229] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3235] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3241] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3247] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3253] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3259] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3271] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3277] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3283] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3289] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3295] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3301] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3307] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3313] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3319] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3325] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3331] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3337] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3343] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3349] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3355] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3361] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3367] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3373] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3379] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3385] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3391] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3397] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3403] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3409] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3415] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3421] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3427] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3433] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3439] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3445] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3451] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3457] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3463] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3469] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3475] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3487] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3493] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [3499] (10,20] (0,10] (10,20] (10,20] (10,20] (0,10]
## [3505] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3511] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3517] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3523] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3529] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3535] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3541] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3547] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3553] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [3559] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3565] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3571] (0,10] (30,45.8] (0,10] (0,10] (0,10] (0,10]
## [3577] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3583] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3589] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3595] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3601] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3607] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3613] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3619] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3625] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [3631] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3637] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3643] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3649] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3655] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3661] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3667] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3673] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3679] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3685] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3691] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3697] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3703] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3709] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3715] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3721] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3727] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3733] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3739] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3745] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3751] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3757] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3763] (0,10] (10,20] (0,10] (0,10] (10,20] (10,20]
## [3769] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3775] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [3781] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3787] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3793] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3799] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3805] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3811] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3817] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3823] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3829] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3835] (0,10] (0,10] (0,10] (0,10] (0,10] (30,45.8]
## [3841] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3847] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3853] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3859] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3865] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3871] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3877] (10,20] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3883] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3889] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3895] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3901] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3907] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3913] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3919] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3925] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3931] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3937] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3943] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3949] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3955] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3961] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3967] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3973] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3979] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3985] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3991] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3997] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4003] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4009] (10,20] (0,10] (10,20] (0,10] (10,20] (10,20]
## [4015] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4021] (0,10] (10,20] (20,30] (0,10] (10,20] (10,20]
## [4027] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4033] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4039] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4045] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4051] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4057] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4063] (10,20] (0,10] (0,10] (10,20] (10,20] (0,10]
## [4069] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4075] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4081] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4087] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4093] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4099] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4105] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4111] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4117] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4123] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4129] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4135] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4141] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4147] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4153] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4159] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4165] (0,10] (10,20] (10,20] (10,20] (0,10] (10,20]
## [4171] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4177] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4183] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4189] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4195] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4201] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4207] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4213] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4219] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4225] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4231] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4237] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4243] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4249] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4255] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4261] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4267] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4273] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4279] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4285] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4291] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4297] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4303] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4309] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4315] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4321] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4327] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4333] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4339] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4345] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [4351] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4357] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4363] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4369] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4375] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4381] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4387] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4393] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4399] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4405] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4411] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4417] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4423] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4429] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4435] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4441] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [4447] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4453] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4459] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4465] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4471] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4477] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4483] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4489] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4495] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4501] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4507] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4513] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4519] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4525] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4531] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4537] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4543] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4549] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4555] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4561] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4567] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [4573] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4579] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4585] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [4591] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4597] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4603] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4609] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4615] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4621] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4627] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4633] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4639] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4645] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4651] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4657] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4663] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4669] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [4675] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4681] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4687] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4693] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4699] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4705] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4711] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4717] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [4723] (10,20] (10,20] (0,10] (0,10] (10,20] (10,20]
## [4729] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4735] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4741] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4747] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4753] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4759] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4765] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4771] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4777] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4783] (10,20] (0,10] (10,20] (10,20] (10,20] (0,10]
## [4789] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4795] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4801] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4807] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4813] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4819] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4825] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4831] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4837] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4843] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4849] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4855] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [4861] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4867] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4873] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4879] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4885] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4891] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4897] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4903] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4909] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4915] (10,20] (10,20] (0,10] (0,10] (0,10] (20,30]
## [4921] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4927] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4933] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4939] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4945] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4951] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4957] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4963] (0,10] (20,30] (10,20] (10,20] (10,20] (0,10]
## [4969] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4975] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4981] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4987] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4993] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4999] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5005] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5011] (10,20] (10,20] (10,20] (10,20] (0,10] (0,10]
## [5017] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5023] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5029] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5035] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5041] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5047] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5053] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5059] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5065] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5071] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5077] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5083] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5089] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5095] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5101] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5107] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5113] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5119] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5125] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5131] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5137] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5143] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5149] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5155] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5161] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5167] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5173] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5179] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5185] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5191] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5197] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5203] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5209] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5215] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5221] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5227] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5233] (0,10] (0,10] (20,30] (0,10] (0,10] (0,10]
## [5239] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5245] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5251] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5257] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5263] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [5269] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5275] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5281] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5287] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5293] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5299] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5305] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5311] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5317] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [5323] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5329] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5335] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5341] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5347] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5353] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5359] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5365] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5371] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5377] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5383] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5389] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5395] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5401] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5407] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5413] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5419] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5425] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5431] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5437] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5443] (0,10] (20,30] (0,10] (0,10] (0,10] (10,20]
## [5449] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5455] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [5461] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5467] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5473] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5479] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5485] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5491] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5497] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5503] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5509] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5515] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5521] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5527] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5533] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5539] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5545] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5551] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5557] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5563] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5569] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5575] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5581] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5587] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5593] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5599] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5605] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5611] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5617] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5623] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5629] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5635] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5641] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5647] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5653] (20,30] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5659] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5665] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5671] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [5677] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5683] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5689] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5695] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5701] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5707] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5713] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5719] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [5725] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [5731] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5737] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5743] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5749] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5755] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5761] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5767] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5773] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5779] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5785] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5791] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5797] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5803] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5809] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5815] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5821] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5827] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5833] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5839] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5845] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5851] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [5857] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5863] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5869] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5875] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5881] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [5887] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5893] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5899] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5905] (10,20] (0,10] (0,10] (10,20] (10,20] (10,20]
## [5911] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5917] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5923] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5929] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5935] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5941] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5947] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5953] (0,10] (10,20] (0,10] (0,10] (10,20] (10,20]
## [5959] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5965] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5971] (10,20] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5977] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5983] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5989] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5995] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6001] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6007] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6013] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6019] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6025] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6031] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6037] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6043] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6049] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [6055] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6061] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6067] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6073] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6079] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6085] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6091] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6097] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6103] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6109] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [6115] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6121] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6127] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6133] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6139] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6145] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [6151] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6157] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6163] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6169] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6175] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6181] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6187] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6193] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6199] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6205] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [6211] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [6217] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6223] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6229] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6235] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6241] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [6247] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6253] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6259] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6271] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6277] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [6283] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6289] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6295] (10,20] (0,10] (0,10] (10,20] (10,20] (10,20]
## [6301] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6307] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6313] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6319] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6325] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6331] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6337] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6343] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6349] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6355] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6361] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6367] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6373] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6379] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6385] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [6391] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6397] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6403] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6409] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6415] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6421] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [6427] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6433] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6439] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6445] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6451] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6457] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6463] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6469] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6475] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [6481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6487] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6493] (0,10] (0,10] (0,10] (0,10] (0,10]
## Levels: (0,10] (10,20] (20,30] (30,45.8]str(Vinhos)## 'data.frame': 6497 obs. of 14 variables:
## $ fixedacidity : num 6.6 6.7 10.6 5.4 6.7 6.8 6.6 7.2 5.1 6.2 ...
## $ volatileacidity : num 0.24 0.34 0.31 0.18 0.3 0.5 0.61 0.66 0.26 0.22 ...
## $ citricacid : num 0.35 0.43 0.49 0.24 0.44 0.11 0 0.33 0.33 0.2 ...
## $ residualsugar : num 7.7 1.6 2.2 4.8 18.8 ...
## $ chlorides : num 0.031 0.041 0.063 0.041 0.057 0.075 0.069 0.068 0.027 0.035 ...
## $ freesulfurdioxide : num 36 29 18 30 65 16 4 34 46 58 ...
## $ totalsulfurdioxide: num 135 114 40 113 224 49 8 102 113 184 ...
## $ density : num 0.994 0.99 0.998 0.994 1 ...
## $ pH : num 3.19 3.23 3.14 3.42 3.11 3.36 3.33 3.27 3.35 3.11 ...
## $ sulphates : num 0.37 0.44 0.51 0.4 0.53 0.79 0.37 0.78 0.43 0.53 ...
## $ alcohol : num 10.5 12.6 9.8 9.4 9.1 9.5 10.4 12.8 11.4 9 ...
## $ quality : int 5 6 6 6 5 5 4 6 7 6 ...
## $ Vinho : Factor w/ 2 levels "RED","WHITE": 2 2 1 2 2 1 1 1 2 2 ...
## $ fx_redSugar : Factor w/ 4 levels "(0,10]","(10,20]",..: 1 1 1 1 2 1 1 1 1 3 ...CrossTable( Vinhos$fx_redSugar , Vinhos$Vinho) ##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 6497
##
##
## | Vinhos$Vinho
## Vinhos$fx_redSugar | RED | WHITE | Row Total |
## -------------------|-----------|-----------|-----------|
## (0,10] | 1588 | 3705 | 5293 |
## | 62.493 | 20.401 | |
## | 0.300 | 0.700 | 0.815 |
## | 0.993 | 0.756 | |
## | 0.244 | 0.570 | |
## -------------------|-----------|-----------|-----------|
## (10,20] | 11 | 1175 | 1186 |
## | 270.305 | 88.244 | |
## | 0.009 | 0.991 | 0.183 |
## | 0.007 | 0.240 | |
## | 0.002 | 0.181 | |
## -------------------|-----------|-----------|-----------|
## (20,30] | 0 | 15 | 15 |
## | 3.692 | 1.205 | |
## | 0.000 | 1.000 | 0.002 |
## | 0.000 | 0.003 | |
## | 0.000 | 0.002 | |
## -------------------|-----------|-----------|-----------|
## (30,45.8] | 0 | 3 | 3 |
## | 0.738 | 0.241 | |
## | 0.000 | 1.000 | 0.000 |
## | 0.000 | 0.001 | |
## | 0.000 | 0.000 | |
## -------------------|-----------|-----------|-----------|
## Column Total | 1599 | 4898 | 6497 |
## | 0.246 | 0.754 | |
## -------------------|-----------|-----------|-----------|
##
## Análise:
Olahndo os intervalos de resíduos de açucar (faixas de 10 em 10), podemos ver que a maior concentração esta na faixa entre 0 e 10 (81,5%)
O mesmo comprtamento se aplica se olharmos por tipo de vinho: Brancos (75,6%) e tintos (99,3%). O que indica que os vinhos tintos tem menos açucar, pois sua concentração esta na faixa de 0 a 10 (faixa inicial) de concentração de resíduo de açucar. E os brancos apresentam maiores concetrações nas faixas superiores: Faixa de 10 a 20, Brancos (24%) x Tintos (0,7%)
attach(Vinhos)## The following objects are masked from Vinhos (pos = 3):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileaciditylibrary(psych)## Warning: package 'psych' was built under R version 3.4.4describe(Vinhos)## vars n mean sd median trimmed mad min max
## fixedacidity 1 6497 7.22 1.30 7.00 7.06 0.89 3.80 15.90
## volatileacidity 2 6497 0.34 0.16 0.29 0.32 0.12 0.08 1.58
## citricacid 3 6497 0.32 0.15 0.31 0.32 0.10 0.00 1.66
## residualsugar 4 6497 5.44 4.73 3.00 4.70 2.52 0.60 45.80
## chlorides 5 6497 0.06 0.04 0.05 0.05 0.02 0.01 0.61
## freesulfurdioxide 6 6497 30.53 17.75 29.00 29.32 17.79 1.00 289.00
## totalsulfurdioxide 7 6497 115.74 56.52 118.00 115.92 57.82 6.00 440.00
## density 8 6497 0.99 0.00 0.99 0.99 0.00 0.99 1.01
## pH 9 6497 3.22 0.16 3.21 3.21 0.16 2.72 4.01
## sulphates 10 6497 0.53 0.15 0.51 0.52 0.12 0.22 2.00
## alcohol 11 6497 10.49 1.22 10.30 10.40 1.33 0.96 14.90
## quality 12 6497 5.82 0.87 6.00 5.79 1.48 3.00 9.00
## Vinho* 13 6497 1.75 0.43 2.00 1.82 0.00 1.00 2.00
## fx_redSugar* 14 6497 1.19 0.40 1.00 1.11 0.00 1.00 4.00
## range skew kurtosis se
## fixedacidity 12.10 1.72 5.05 0.02
## volatileacidity 1.50 1.49 2.82 0.00
## citricacid 1.66 0.47 2.39 0.00
## residualsugar 45.20 1.24 1.28 0.06
## chlorides 0.60 5.40 50.84 0.00
## freesulfurdioxide 288.00 1.22 7.90 0.22
## totalsulfurdioxide 434.00 0.00 -0.37 0.70
## density 0.03 0.05 -0.32 0.00
## pH 1.29 0.39 0.37 0.00
## sulphates 1.78 1.80 8.64 0.00
## alcohol 13.94 0.26 1.56 0.02
## quality 6.00 0.19 0.23 0.01
## Vinho* 1.00 -1.18 -0.61 0.01
## fx_redSugar* 3.00 1.81 2.20 0.00# describe
# A data.frame of the relevant statistics:
# item name
# item number
# number of valid cases
# mean
# standard deviation
# trimmed mean (with trim defaulting to .1)
# median (standard or interpolated
# mad: median absolute deviation (from the median)
# minimum
# maximum
# skew
# kurtosis
# standard error
summary(Vinhos)## fixedacidity volatileacidity citricacid residualsugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.60
## 1st Qu.: 6.400 1st Qu.:0.2300 1st Qu.:0.2500 1st Qu.: 1.80
## Median : 7.000 Median :0.2900 Median :0.3100 Median : 3.00
## Mean : 7.215 Mean :0.3397 Mean :0.3186 Mean : 5.44
## 3rd Qu.: 7.700 3rd Qu.:0.4000 3rd Qu.:0.3900 3rd Qu.: 8.10
## Max. :15.900 Max. :1.5800 Max. :1.6600 Max. :45.80
## chlorides freesulfurdioxide totalsulfurdioxide density
## Min. :0.00900 Min. : 1.00 Min. : 6.0 Min. :0.9871
## 1st Qu.:0.03800 1st Qu.: 17.00 1st Qu.: 77.0 1st Qu.:0.9923
## Median :0.04700 Median : 29.00 Median :118.0 Median :0.9949
## Mean :0.05603 Mean : 30.53 Mean :115.7 Mean :0.9947
## 3rd Qu.:0.06500 3rd Qu.: 41.00 3rd Qu.:156.0 3rd Qu.:0.9970
## Max. :0.61100 Max. :289.00 Max. :440.0 Max. :1.0140
## pH sulphates alcohol quality
## Min. :2.720 Min. :0.2200 Min. : 0.9567 Min. :3.000
## 1st Qu.:3.110 1st Qu.:0.4300 1st Qu.: 9.5000 1st Qu.:5.000
## Median :3.210 Median :0.5100 Median :10.3000 Median :6.000
## Mean :3.219 Mean :0.5313 Mean :10.4862 Mean :5.818
## 3rd Qu.:3.320 3rd Qu.:0.6000 3rd Qu.:11.3000 3rd Qu.:6.000
## Max. :4.010 Max. :2.0000 Max. :14.9000 Max. :9.000
## Vinho fx_redSugar
## RED :1599 (0,10] :5293
## WHITE:4898 (10,20] :1186
## (20,30] : 15
## (30,45.8]: 3
##
## white <- subset(Vinhos, Vinho=="WHITE", select=c(quality,fixedacidity,volatileacidity,citricacid,residualsugar,
chlorides,freesulfurdioxide,totalsulfurdioxide,density,pH,
sulphates,alcohol))Análise:
Criamos um Dataset para os vinhos Brancos, com todas as variáveis usadas anteriormente
#EstatÌsticas descritivas
summary(white)## quality fixedacidity volatileacidity citricacid
## Min. :3.000 Min. : 3.800 Min. :0.0800 Min. :0.0000
## 1st Qu.:5.000 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700
## Median :6.000 Median : 6.800 Median :0.2600 Median :0.3200
## Mean :5.878 Mean : 6.855 Mean :0.2782 Mean :0.3342
## 3rd Qu.:6.000 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900
## Max. :9.000 Max. :14.200 Max. :1.1000 Max. :1.6600
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median : 5.200 Median :0.04300 Median : 34.00 Median :134.0
## Mean : 6.387 Mean :0.04577 Mean : 35.31 Mean :138.4
## 3rd Qu.: 9.900 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :45.800 Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4898 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0140 Max. :3.820 Max. :1.0800 Max. :14.20str(white)## 'data.frame': 4898 obs. of 12 variables:
## $ quality : int 5 6 6 5 7 6 5 6 6 6 ...
## $ fixedacidity : num 6.6 6.7 5.4 6.7 5.1 6.2 6.6 7.3 6.7 6.2 ...
## $ volatileacidity : num 0.24 0.34 0.18 0.3 0.26 0.22 0.25 0.27 0.26 0.12 ...
## $ citricacid : num 0.35 0.43 0.24 0.44 0.33 0.2 0.36 0.37 0.29 0.26 ...
## $ residualsugar : num 7.7 1.6 4.8 18.8 1.1 ...
## $ chlorides : num 0.031 0.041 0.041 0.057 0.027 0.035 0.045 0.042 0.038 0.044 ...
## $ freesulfurdioxide : num 36 29 30 65 46 58 54 36 40 56 ...
## $ totalsulfurdioxide: num 135 114 113 224 113 184 180 130 179 158 ...
## $ density : num 0.994 0.99 0.994 1 0.989 ...
## $ pH : num 3.19 3.23 3.42 3.11 3.35 3.11 3.08 3.48 3.23 3.52 ...
## $ sulphates : num 0.37 0.44 0.4 0.53 0.43 0.53 0.42 0.75 0.56 0.37 ...
## $ alcohol : num 10.5 12.6 9.4 9.1 11.4 9 9.2 9.9 10.4 10.5 ...Análise:
Olhando as estatísticas básicas de todas as proprieddes dos vinhos brancos, podemos perceber alguns pontos:
Médias próximas as medianas, que indica possível simetria nas distribuições para: fixedacidity, volatileacidity, citricacid, chlorides, freesulfurdioxide, totalsulfurdioxide, density, pH, sulphates, alcohol e quality.
Avaliando os valores máximos e mínimos, temos indícios de outliers para: citricacid (mínimo e máximo), residualsugar (máximo), freesulfurdioxide (máximo).
attach(white)## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 8):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity#EstatÌsticas descritivas
par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(quality, main='quality')
Análise:
Todos os Box Plots dos vinhos brancos apresentarem Outliers (exceto a variavel alcohol), que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide, citricacid e freesulfurdioxide com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.
Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.
boxplot.stats(white$residualsugar)## $stats
## [1] 0.6 1.7 5.2 9.9 22.0
##
## $n
## [1] 4898
##
## $conf
## [1] 5.014877 5.385123
##
## $out
## [1] 26.05 31.60 22.60 45.80 31.60 26.05 23.50AIQ_residualsugar<-quantile(white$residualsugar,.75,type=2)-quantile(white$residualsugar,.25,type=2)
AIQ_residualsugar## 75%
## 8.2limsup_residualsugar= quantile(white$residualsugar,.75,type=4)+1.5*AIQ_residualsugar
limsup_residualsugar## 75%
## 22.2liminf_residualsugar= quantile(white$residualsugar,.25,type=2)-1.5*AIQ_residualsugar
liminf_residualsugar## 25%
## -10.6Análise:
Sobre as estatísticas do BoxPlot (boxplot.stat) podemos dizer: - O bigode inferiro = valor mínimo (0,6), os qurtis Q1 = 1,7 e Q2 (mediana) = 5,2 e Q3 = 9,9. O bigode superior = 22,0. Como temos valores maiores que o 22,0, teremos outliers acima de 22,0. Mostrado no $out. - Os valores do $conf, são (segundo Chambers e McGill) aproximadamente o intervalo de confiança para a mediana.
Temos também a amplitude entre quartis: Q3 - Q1 = 8,2
#excluir outliers
plot(quality~residualsugar)
white1<-subset(white, residualsugar<=22.2)
#fix(white1)Análise:
Analisando o gráfico do residuo de açucar (resildualsugar) x nota de qualidade dos vinhos brancos (quality), podemos perceber uma maior concentração de resíduos de açucar para os vinhos com notas entre 5 e 6
attach(white1)## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 7):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 9):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileaciditysummary(white1)## quality fixedacidity volatileacidity citricacid
## Min. :3.000 Min. : 3.800 Min. :0.080 Min. :0.0000
## 1st Qu.:5.000 1st Qu.: 6.300 1st Qu.:0.210 1st Qu.:0.2700
## Median :6.000 Median : 6.800 Median :0.260 Median :0.3200
## Mean :5.878 Mean : 6.854 Mean :0.278 Mean :0.3341
## 3rd Qu.:6.000 3rd Qu.: 7.300 3rd Qu.:0.320 3rd Qu.:0.3900
## Max. :9.000 Max. :14.200 Max. :1.100 Max. :1.6600
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median : 5.200 Median :0.04300 Median : 34.00 Median :134.0
## Mean : 6.354 Mean :0.04575 Mean : 35.31 Mean :138.3
## 3rd Qu.: 9.850 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :22.000 Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4899 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0024 Max. :3.820 Max. :1.0800 Max. :14.20plot(residualsugar,alcohol)
abline(v=mean(residualsugar), col="red")
abline(h=mean(alcohol), col="green")
Análise:
Após tirarmos o valor de residualsugar acima de 22,2 (7 valores acima do limite do bigode do BoxPlot), podemos analisar que existe uma correlação negativa entre as variáveis, ou seja quanto maior o teor alcolico, menor a concentração de resíduo de açucar, com exceção de valores de baixo resíduo de açucar e baixa quantidade de alcool, que possivelmente pode ser explicado por não ter açucar suficiente no início do processo (suco de uva) e que não provoca uma fermentação que eleve o nível de alcool no vinho.
Ainda observando que estes valores de residuo de açucar baixo e alcool baixo, reduzem os valores de média para as duas variáveis, podendo enviezar a interpretação de uma futura análise de regressão.
A base de dados white1 é a base de vinhos brancos sem os Outliers, que será usada a partir de agora
# matriz de correlaÁıes
matcor <- cor(white1)
print(matcor, digits = 2)## quality fixedacidity volatileacidity citricacid
## quality 1.0000 -0.114 -0.1963 -0.0088
## fixedacidity -0.1141 1.000 -0.0248 0.2895
## volatileacidity -0.1963 -0.025 1.0000 -0.1529
## citricacid -0.0088 0.290 -0.1529 1.0000
## residualsugar -0.0995 0.087 0.0460 0.0914
## chlorides -0.2095 0.023 0.0700 0.1132
## freesulfurdioxide 0.0088 -0.049 -0.0949 0.0943
## totalsulfurdioxide -0.1746 0.091 0.0892 0.1207
## density -0.3176 0.268 0.0032 0.1483
## pH 0.0991 -0.427 -0.0334 -0.1643
## sulphates 0.0535 -0.017 -0.0379 0.0616
## alcohol 0.4363 -0.120 0.0673 -0.0765
## residualsugar chlorides freesulfurdioxide
## quality -0.100 -0.210 0.00876
## fixedacidity 0.087 0.023 -0.04884
## volatileacidity 0.046 0.070 -0.09485
## citricacid 0.091 0.113 0.09425
## residualsugar 1.000 0.086 0.30987
## chlorides 0.086 1.000 0.10095
## freesulfurdioxide 0.310 0.101 1.00000
## totalsulfurdioxide 0.408 0.199 0.61591
## density 0.831 0.261 0.30898
## pH -0.199 -0.091 0.00018
## sulphates -0.028 0.017 0.06009
## alcohol -0.462 -0.362 -0.25022
## totalsulfurdioxide density pH sulphates alcohol
## quality -0.1746 -0.3176 0.09913 0.053 0.436
## fixedacidity 0.0905 0.2682 -0.42667 -0.017 -0.120
## volatileacidity 0.0892 0.0032 -0.03342 -0.038 0.067
## citricacid 0.1207 0.1483 -0.16430 0.062 -0.077
## residualsugar 0.4081 0.8315 -0.19916 -0.028 -0.462
## chlorides 0.1990 0.2613 -0.09063 0.017 -0.362
## freesulfurdioxide 0.6159 0.3090 0.00018 0.060 -0.250
## totalsulfurdioxide 1.0000 0.5436 0.00274 0.135 -0.448
## density 0.5436 1.0000 -0.09845 0.075 -0.806
## pH 0.0027 -0.0984 1.00000 0.155 0.121
## sulphates 0.1348 0.0748 0.15517 1.000 -0.018
## alcohol -0.4484 -0.8064 0.12103 -0.018 1.000Análise:
Observando as correlações, algumas nos chamam a atenção: - residualsugar x density = 0,8315, que comprova que vinhos com muito açucar tem maior densidade, no sentido inverso; - vinhos com muito alcool tem menor densidade (correlação = -0,8064). - forte correlação entre freesulfurdioxide x totalsulfurdioxide (0,61591), devido ao livre fazer parte do total deste conservante.
#install.packages(corrgram)
#library(corrgram)
#corrgram (matcor, type = "cor", lower.panel = panel.shade, upper.panel = panel.pie)
panel.cor <- function(x, y, digits=2, prefix ="", cex.cor,
...) {
usr <- par("usr")
on.exit(par(usr))
par(usr = c(0, 1, 0, 1))
r <- cor(x, y , use = "pairwise.complete.obs")
txt <- format(c(r, 0.123456789), digits = digits) [1]
txt <- paste(prefix, txt, sep = "")
if (missing(cex.cor))
cex <- 0.8/strwidth(txt)
# abs(r) È para que na saÌda as correlaÁıes ficam proporcionais
text(0.5, 0.5, txt, cex = cex * abs(r))
}
#pdf(file = "grafico.pdf")
pairs(white1, lower.panel=panel.smooth, upper.panel=panel.cor)
Análise:
Agora podemos comprovar atraves de gráficos o que já foi comentado a análise da tabela de correlação
#avaliar inicio
dados_normalizados = as.data.frame(scale(white1))
names(dados_normalizados)## [1] "quality" "fixedacidity" "volatileacidity"
## [4] "citricacid" "residualsugar" "chlorides"
## [7] "freesulfurdioxide" "totalsulfurdioxide" "density"
## [10] "pH" "sulphates" "alcohol"summary(dados_normalizados)## quality fixedacidity volatileacidity citricacid
## Min. :-3.2482 Min. :-3.61898 Min. :-1.9740 Min. :-2.7613
## 1st Qu.:-0.9910 1st Qu.:-0.65685 1st Qu.:-0.6781 1st Qu.:-0.5299
## Median : 0.1375 Median :-0.06443 Median :-0.1797 Median :-0.1167
## Mean : 0.0000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.1375 3rd Qu.: 0.52800 3rd Qu.: 0.4184 3rd Qu.: 0.4617
## Max. : 3.5232 Max. : 8.70347 Max. : 8.1937 Max. :10.9572
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. :-1.1623 Min. :-1.6835 Min. :-1.95836 Min. :-3.0434
## 1st Qu.:-0.9401 1st Qu.:-0.4467 1st Qu.:-0.72367 1st Qu.:-0.7137
## Median :-0.2331 Median :-0.1261 Median :-0.07692 Median :-0.1019
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.7062 3rd Qu.: 0.1946 3rd Qu.: 0.62862 3rd Qu.: 0.6746
## Max. : 3.1604 Max. :13.7533 Max. :14.91577 Max. : 7.0987
## density pH sulphates
## Min. :-2.38090 Min. :-3.10123 Min. :-2.3651
## 1st Qu.:-0.78919 1st Qu.:-0.65126 1st Qu.:-0.7002
## Median :-0.09519 Median :-0.05532 Median :-0.1745
## Mean : 0.00000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.72311 3rd Qu.: 0.60684 3rd Qu.: 0.5265
## Max. : 2.90178 Max. : 4.18247 Max. : 5.1706
## alcohol
## Min. :-2.04414
## 1st Qu.:-0.82479
## Median :-0.09317
## Mean : 0.00000
## 3rd Qu.: 0.71973
## Max. : 2.99587describe(dados_normalizados)## vars n mean sd median trimmed mad min max range
## quality 1 4891 0 1 0.14 -0.03 1.67 -3.25 3.52 6.77
## fixedacidity 2 4891 0 1 -0.06 -0.05 0.88 -3.62 8.70 12.32
## volatileacidity 3 4891 0 1 -0.18 -0.11 0.89 -1.97 8.19 10.17
## citricacid 4 4891 0 1 -0.12 -0.07 0.74 -2.76 10.96 13.72
## residualsugar 5 4891 0 1 -0.23 -0.11 1.08 -1.16 3.16 4.32
## chlorides 6 4891 0 1 -0.13 -0.13 0.48 -1.68 13.75 15.44
## freesulfurdioxide 7 4891 0 1 -0.08 -0.06 0.96 -1.96 14.92 16.87
## totalsulfurdioxide 8 4891 0 1 -0.10 -0.03 1.01 -3.04 7.10 10.14
## density 9 4891 0 1 -0.10 -0.03 1.09 -2.38 2.90 5.28
## pH 10 4891 0 1 -0.06 -0.04 0.98 -3.10 4.18 7.28
## sulphates 11 4891 0 1 -0.17 -0.09 0.91 -2.37 5.17 7.54
## alcohol 12 4891 0 1 -0.09 -0.07 1.21 -2.04 3.00 5.04
## skew kurtosis se
## quality 0.16 0.21 0.01
## fixedacidity 0.65 2.17 0.01
## volatileacidity 1.54 4.81 0.01
## citricacid 1.28 6.18 0.01
## residualsugar 0.73 -0.52 0.01
## chlorides 5.03 37.68 0.01
## freesulfurdioxide 1.41 11.46 0.01
## totalsulfurdioxide 0.39 0.57 0.01
## density 0.25 -0.76 0.01
## pH 0.46 0.53 0.01
## sulphates 0.98 1.59 0.01
## alcohol 0.49 -0.70 0.01Análise:
Criamos a base de dados “dados_normalizados” normalizando (subtraindo a média e dividindo pelo desvio padrão) para uso posterior
# componentes principais - básico
pca1 <- princomp(white1[complete.cases(white1),], cor=TRUE)
summary(pca1)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.8376211 1.2601782 1.1725041 1.04144219 0.98963356
## Proportion of Variance 0.2814043 0.1323374 0.1145638 0.09038349 0.08161455
## Cumulative Proportion 0.2814043 0.4137417 0.5283055 0.61868901 0.70030356
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.96393790 0.87026920 0.84619866 0.74637002
## Proportion of Variance 0.07743136 0.06311404 0.05967101 0.04642235
## Cumulative Proportion 0.77773492 0.84084896 0.90051997 0.94694232
## Comp.10 Comp.11 Comp.12
## Standard deviation 0.5812201 0.53360218 0.118928612
## Proportion of Variance 0.0281514 0.02372761 0.001178668
## Cumulative Proportion 0.9750937 0.99882133 1.000000000Análise:
Avaiando proposção acumulada das componentes principais (28,14%, 41,37%, …) observamos que não houve grande ganho com relação as variáveis originais, como era esperado, já que não existem muita correlação entre as variáveis da nossa base
Vamos usar a metodologia de Compenetes Principais para algumas variáveis que apresentaram alguma correlação: residualsugar, density e alcohol. Para isso criaremos uma base de dados “white1pca” somente com estas variáveis
# componentes principais - Variáveias alta correlação
white1pca <- white1[,c(-1, -2, -3, -4, -6, -7, -8, -10, -11)]
pca2 <- princomp(white1pca[complete.cases(white1pca),], cor = TRUE)
summary(pca2)## Importance of components:
## Comp.1 Comp.2 Comp.3
## Standard deviation 1.553126 0.7335335 0.22299680
## Proportion of Variance 0.804067 0.1793571 0.01657586
## Cumulative Proportion 0.804067 0.9834241 1.00000000dados_normalizados1 <- as.data.frame(scale(white1pca))Análise:
Como era esperado, o uso de PCA para as variáveis: residualsugar, density e alcohol apresentou bom resuldado já que estas tem alta correlação entre si. A proposção acumulada já é de 80,40% na primeria componete
library(psych)
# Escolher os componentes principais
fa.parallel (white1pca, fa="pc", show.legend=FALSE, main = "Eigenvalues dos componentes
principais")## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A loading greater than abs(1) was detected. Examine the loadings
## carefully.## The estimated weights for the factor scores are probably incorrect. Try a different factor extraction method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : An ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = NA and the number of components = 1Análise:
Como visto anteriormente, escolheremos a 1a compenente principal pois ele sozinha já explica/consolida grnade parte da informação das e variáveis
# Rotação varimax
library(psych)
# Varimax Rotated Principal Components
# # extrair os fatores
vinhospca <- principal(white1pca, nfactors=1, scores=T, rotate="varimax")
vinhospca # print results ## Principal Components Analysis
## Call: principal(r = white1pca, nfactors = 1, rotate = "varimax", scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 h2 u2 com
## residualsugar 0.86 0.73 0.27 1
## density 0.98 0.97 0.03 1
## alcohol -0.84 0.71 0.29 1
##
## PC1
## SS loadings 2.41
## Proportion Var 0.80
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.15
## with the empirical chi square 661.34 with prob < NA
##
## Fit based upon off diagonal values = 0.96fator01 = vinhospca$scores[,1]
hist(fator01)
white1<-cbind(white1,fator01)
#fix(matriz)
plot(quality,fator01)
matcor <- cor(white1)
print(matcor, digits = 2)## quality fixedacidity volatileacidity citricacid
## quality 1.0000 -0.114 -0.1963 -0.0088
## fixedacidity -0.1141 1.000 -0.0248 0.2895
## volatileacidity -0.1963 -0.025 1.0000 -0.1529
## citricacid -0.0088 0.290 -0.1529 1.0000
## residualsugar -0.0995 0.087 0.0460 0.0914
## chlorides -0.2095 0.023 0.0700 0.1132
## freesulfurdioxide 0.0088 -0.049 -0.0949 0.0943
## totalsulfurdioxide -0.1746 0.091 0.0892 0.1207
## density -0.3176 0.268 0.0032 0.1483
## pH 0.0991 -0.427 -0.0334 -0.1643
## sulphates 0.0535 -0.017 -0.0379 0.0616
## alcohol 0.4363 -0.120 0.0673 -0.0765
## fator01 -0.3174 0.182 -0.0058 0.1197
## residualsugar chlorides freesulfurdioxide
## quality -0.100 -0.210 0.00876
## fixedacidity 0.087 0.023 -0.04884
## volatileacidity 0.046 0.070 -0.09485
## citricacid 0.091 0.113 0.09425
## residualsugar 1.000 0.086 0.30987
## chlorides 0.086 1.000 0.10095
## freesulfurdioxide 0.310 0.101 1.00000
## totalsulfurdioxide 0.408 0.199 0.61591
## density 0.831 0.261 0.30898
## pH -0.199 -0.091 0.00018
## sulphates -0.028 0.017 0.06009
## alcohol -0.462 -0.362 -0.25022
## fator01 0.856 0.264 0.32348
## totalsulfurdioxide density pH sulphates alcohol
## quality -0.1746 -0.3176 0.09913 0.053 0.436
## fixedacidity 0.0905 0.2682 -0.42667 -0.017 -0.120
## volatileacidity 0.0892 0.0032 -0.03342 -0.038 0.067
## citricacid 0.1207 0.1483 -0.16430 0.062 -0.077
## residualsugar 0.4081 0.8315 -0.19916 -0.028 -0.462
## chlorides 0.1990 0.2613 -0.09063 0.017 -0.362
## freesulfurdioxide 0.6159 0.3090 0.00018 0.060 -0.250
## totalsulfurdioxide 1.0000 0.5436 0.00274 0.135 -0.448
## density 0.5436 1.0000 -0.09845 0.075 -0.806
## pH 0.0027 -0.0984 1.00000 0.155 0.121
## sulphates 0.1348 0.0748 0.15517 1.000 -0.018
## alcohol -0.4484 -0.8064 0.12103 -0.018 1.000
## fator01 0.5233 0.9849 -0.15312 0.027 -0.843
## fator01
## quality -0.3174
## fixedacidity 0.1823
## volatileacidity -0.0058
## citricacid 0.1197
## residualsugar 0.8557
## chlorides 0.2636
## freesulfurdioxide 0.3235
## totalsulfurdioxide 0.5233
## density 0.9849
## pH -0.1531
## sulphates 0.0270
## alcohol -0.8425
## fator01 1.0000#attach(matriz)
#write.table(file='E:/LabBDT2018/Analise_vinhos.csv',matriz, sep=';',dec=',')Análise:
Incluimos no banco de dados white1 uma coluna fator01 que é a combinação , via método PCA, das variáveis residualsugar, density e alcohol. O fator01 poderá substituir estas 3 variáveis em outros modelos com pequenas perdas, tendo um modelo redizido (menos variáveis).
Podemos verificar isso olhando as correlações: altas entre o fator01 e as 3 variáveis (residualsugar 85,57%, density 98,49% e alcohol -84,25%) e no mesmo paramar com a variável de resposta quality -31,74% que as outras 3
Partindo agora para os modelos de predição
Começamos com regressão linerar
attach(white1)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white1 (pos = 3):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 7):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 8):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 10):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidityModelo1 <- lm(quality ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)
summary(Modelo1)##
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + citricacid +
## residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide +
## density + pH + sulphates + alcohol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8860 -0.4972 -0.0425 0.4624 3.1111
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.255e+02 2.336e+01 9.652 < 2e-16 ***
## fixedacidity 1.198e-01 2.319e-02 5.165 2.49e-07 ***
## volatileacidity -1.880e+00 1.135e-01 -16.560 < 2e-16 ***
## citricacid 3.698e-02 9.552e-02 0.387 0.698666
## residualsugar 1.061e-01 8.735e-03 12.148 < 2e-16 ***
## chlorides 7.384e-02 5.474e-01 0.135 0.892707
## freesulfurdioxide 3.450e-03 8.435e-04 4.090 4.38e-05 ***
## totalsulfurdioxide 8.962e-05 3.837e-04 0.234 0.815337
## density -2.264e+02 2.367e+01 -9.566 < 2e-16 ***
## pH 9.097e-01 1.130e-01 8.051 1.02e-15 ***
## sulphates 7.204e-01 1.015e-01 7.096 1.47e-12 ***
## alcohol 1.037e-01 2.958e-02 3.505 0.000461 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7489 on 4879 degrees of freedom
## Multiple R-squared: 0.2873, Adjusted R-squared: 0.2857
## F-statistic: 178.8 on 11 and 4879 DF, p-value: < 2.2e-16Análise:
O modelo com todas as variáveis tem um R2 Ajustado de 28,57% e Residual Standard Error de 0,7489 Parametros para escolher o melhor modelo é um maior R2 ajustado e/ou um menor Residual Standard Error
Com temos alguma variáveis com alto p-Valor, valor tira-los do modelo (citricacid, chlorides, totalsulfurdioxide), abaixo
Modelo2 <- lm(quality ~ fixedacidity+volatileacidity+residualsugar+freesulfurdioxide+density+pH+sulphates+alcohol)
summary(Modelo2)##
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + residualsugar +
## freesulfurdioxide + density + pH + sulphates + alcohol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8969 -0.4944 -0.0422 0.4617 3.1110
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 222.6060716 22.0610591 10.090 < 2e-16 ***
## fixedacidity 0.1193286 0.0225543 5.291 1.27e-07 ***
## volatileacidity -1.8801511 0.1092153 -17.215 < 2e-16 ***
## residualsugar 0.1051611 0.0083239 12.634 < 2e-16 ***
## freesulfurdioxide 0.0035924 0.0006757 5.317 1.10e-07 ***
## density -223.4943952 22.3350205 -10.006 < 2e-16 ***
## pH 0.8998353 0.1100877 8.174 3.77e-16 ***
## sulphates 0.7219599 0.1012550 7.130 1.15e-12 ***
## alcohol 0.1059325 0.0291161 3.638 0.000277 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7487 on 4882 degrees of freedom
## Multiple R-squared: 0.2873, Adjusted R-squared: 0.2861
## F-statistic: 246 on 8 and 4882 DF, p-value: < 2.2e-16Análise:
O modelo sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% (levemente melhor que o anterior) e Residual Standard Error de 0,7487 (leventente melhor que o anterior), mas com um modelo com menos variáveis
Agora vamos testar um modelo com o PCA trabalhado acima fator01, tirando as variáveis que o compoem (residualsugar, density e alcohol)
Modelo3 <- lm(quality ~ fixedacidity+volatileacidity+freesulfurdioxide+pH+sulphates+fator01)
summary(Modelo3)##
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + freesulfurdioxide +
## pH + sulphates + fator01)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3985 -0.5299 -0.0473 0.5246 3.4903
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.0443781 0.3371370 17.929 < 2e-16 ***
## fixedacidity -0.0473671 0.0155284 -3.050 0.002298 **
## volatileacidity -1.6608174 0.1170109 -14.194 < 2e-16 ***
## freesulfurdioxide 0.0050022 0.0007339 6.816 1.05e-11 ***
## pH 0.0833160 0.0869460 0.958 0.337984
## sulphates 0.3631688 0.1038230 3.498 0.000473 ***
## fator01 -0.3016249 0.0126504 -23.843 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8151 on 4884 degrees of freedom
## Multiple R-squared: 0.1548, Adjusted R-squared: 0.1538
## F-statistic: 149.1 on 6 and 4884 DF, p-value: < 2.2e-16Análise:
O modelo com PCA tem um R2 Ajustado de 15,38% (pior que o anterior) e Residual Standard Error de 0,8151 (pior que o anterior), mas com um modelo com menos variáveis. Não avaliamos como boa este modelo.
Agora vamos testar um modelo com o PCA trabalhado acima fator01, tirando as variáveis que o compoem (residualsugar, density e alcohol) e também as não significativas no modelo acima (pH)
Modelo4 <- lm(quality ~ fixedacidity+volatileacidity+freesulfurdioxide+sulphates+fator01)
summary(Modelo4)##
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + freesulfurdioxide +
## sulphates + fator01)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3839 -0.5296 -0.0442 0.5216 3.5062
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.3454655 0.1222127 51.921 < 2e-16 ***
## fixedacidity -0.0534901 0.0141526 -3.780 0.000159 ***
## volatileacidity -1.6657118 0.1168984 -14.249 < 2e-16 ***
## freesulfurdioxide 0.0049974 0.0007338 6.810 1.09e-11 ***
## sulphates 0.3796090 0.1023948 3.707 0.000212 ***
## fator01 -0.3026365 0.0126061 -24.007 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8151 on 4885 degrees of freedom
## Multiple R-squared: 0.1547, Adjusted R-squared: 0.1538
## F-statistic: 178.8 on 5 and 4885 DF, p-value: < 2.2e-16Análise:
O modelo com PCA e sem pH tem um R2 Ajustado de 15,38% (igual o anterior) e Residual Standard Error de 0,8151 (igual o anterior), mas com um modelo com menos variáveis. Não avaliamos como boa este modelo e descartaremos o uso de PCA nesta regressão
Sendo assim, avaliamos que o melhor modelo é o 2: Sem PCA e com somente as varíaveis que foram significativas. O modelo sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% e Residual Standard Error de 0,7487, mas com um modelo com menos variáveis
Vamos agora avaliar como o método Stepwise escolheria quais as variáveis que este modelo de previsão, iniciando com todos as variáveis
step(Modelo1)## Start: AIC=-2816.85
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar +
## chlorides + freesulfurdioxide + totalsulfurdioxide + density +
## pH + sulphates + alcohol
##
## Df Sum of Sq RSS AIC
## - chlorides 1 0.010 2736.2 -2818.8
## - totalsulfurdioxide 1 0.031 2736.2 -2818.8
## - citricacid 1 0.084 2736.3 -2818.7
## <none> 2736.2 -2816.8
## - alcohol 1 6.888 2743.1 -2806.6
## - freesulfurdioxide 1 9.382 2745.6 -2802.1
## - fixedacidity 1 14.964 2751.2 -2792.2
## - sulphates 1 28.238 2764.4 -2768.6
## - pH 1 36.353 2772.5 -2754.3
## - density 1 51.317 2787.5 -2728.0
## - residualsugar 1 82.755 2818.9 -2673.1
## - volatileacidity 1 153.788 2890.0 -2551.4
##
## Step: AIC=-2818.83
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar +
## freesulfurdioxide + totalsulfurdioxide + density + pH + sulphates +
## alcohol
##
## Df Sum of Sq RSS AIC
## - totalsulfurdioxide 1 0.030 2736.2 -2820.8
## - citricacid 1 0.091 2736.3 -2820.7
## <none> 2736.2 -2818.8
## - alcohol 1 6.912 2743.1 -2808.5
## - freesulfurdioxide 1 9.413 2745.6 -2804.0
## - fixedacidity 1 15.336 2751.5 -2793.5
## - sulphates 1 28.251 2764.4 -2770.6
## - pH 1 37.318 2773.5 -2754.6
## - density 1 52.642 2788.8 -2727.6
## - residualsugar 1 86.021 2822.2 -2669.4
## - volatileacidity 1 155.126 2891.3 -2551.1
##
## Step: AIC=-2820.77
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar +
## freesulfurdioxide + density + pH + sulphates + alcohol
##
## Df Sum of Sq RSS AIC
## - citricacid 1 0.095 2736.3 -2822.6
## <none> 2736.2 -2820.8
## - alcohol 1 7.186 2743.4 -2809.9
## - fixedacidity 1 15.389 2751.6 -2795.3
## - freesulfurdioxide 1 15.558 2751.8 -2795.0
## - sulphates 1 28.355 2764.6 -2772.3
## - pH 1 37.417 2773.6 -2756.3
## - density 1 56.027 2792.2 -2723.6
## - residualsugar 1 89.342 2825.6 -2665.6
## - volatileacidity 1 160.569 2896.8 -2543.9
##
## Step: AIC=-2822.6
## quality ~ fixedacidity + volatileacidity + residualsugar + freesulfurdioxide +
## density + pH + sulphates + alcohol
##
## Df Sum of Sq RSS AIC
## <none> 2736.3 -2822.6
## - alcohol 1 7.419 2743.7 -2811.4
## - fixedacidity 1 15.689 2752.0 -2796.6
## - freesulfurdioxide 1 15.844 2752.2 -2796.4
## - sulphates 1 28.495 2764.8 -2773.9
## - pH 1 37.447 2773.8 -2758.1
## - density 1 56.122 2792.4 -2725.3
## - residualsugar 1 89.459 2825.8 -2667.3
## - volatileacidity 1 166.107 2902.4 -2536.4##
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + residualsugar +
## freesulfurdioxide + density + pH + sulphates + alcohol)
##
## Coefficients:
## (Intercept) fixedacidity volatileacidity
## 222.606072 0.119329 -1.880151
## residualsugar freesulfurdioxide density
## 0.105161 0.003592 -223.494395
## pH sulphates alcohol
## 0.899835 0.721960 0.105932Análise:
A conclusão é a mesma do Modelo2. O que confirma o que fizemos até agora.
O modelo sem PCA e sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% (levemente melhor que o anterior) e Residual Standard Error de 0,7487 (leventente melhor que o anterior), mas com um modelo com menos variáveis
Vamos agora analisar os resíduos: contra os valores ajustados, sua normalidade e aleatoriedade
library(lmtest)## Warning: package 'lmtest' was built under R version 3.4.4## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.4.4##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericplot(Modelo2, which = 1)
plot(Modelo2, which = 2)
dwtest (Modelo2$residuals ~ Modelo2$fitted.values)##
## Durbin-Watson test
##
## data: Modelo2$residuals ~ Modelo2$fitted.values
## DW = 1.9562, p-value = 0.06256
## alternative hypothesis: true autocorrelation is greater than 0Análise:
Temos alguns pontos (resíduos) um pouco grandes (> 3) para valores ajustados maiores (>6), que também aparecem nas caudas do gráfico de probabilidade Normal. O teste de DW para aleatoriedade tem P-valor um pouco acima de 5% (6,2%)
Com isso ficaremos com este modelo, com atenção ao comportamento de previsão para notas de qualidade >6
Vamos agora para análises pela árvore de regressão
## Árvore de Regressão
attach(white1)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white1 (pos = 5):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 9):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 10):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 11):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 13):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity#install.packages("rpart")
#install.packages("rpart.plot")
library(rpart)
library(rpart.plot)## Warning: package 'rpart.plot' was built under R version 3.4.4modelo_Valor_tree <- rpart (quality ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, cp = 0.001,minsplit = 5,maxdepth=10)
# Faz o Gráfico
rpart.plot(modelo_Valor_tree, type=0, extra="auto", under=TRUE, clip.right.labs=TRUE,
fallen.leaves=FALSE, digits=2, varlen=-10, faclen=20,
cex=0.4, tweak=1.7,
compress=TRUE,
snip=FALSE)## Warning: labs do not fit even at cex 0.15, there may be some overplotting## Warning: cex and tweak both specified, applying both
Val_pred_tree <- predict(modelo_Valor_tree,interval = "prediction", level = 0.95)
str(Val_pred_tree)## Named num [1:4891] 5.72 6.41 5.88 5.31 6.39 ...
## - attr(*, "names")= chr [1:4891] "1" "2" "3" "4" ...mse_tree <- mean((quality - Val_pred_tree)^2)
sqrt(mse_tree)## [1] 0.5914769# grafico residuo
rs <- Val_pred_tree- quality
plot(predict(modelo_Valor_tree), rs, xlab = "Com Árvore de Regressão",ylab = "Residuos")
abline(h = 0, lty = 2)
qqnorm(rs)
qqline(rs)
dwtest (rs ~ Val_pred_tree)##
## Durbin-Watson test
##
## data: rs ~ Val_pred_tree
## DW = 1.9183, p-value = 0.002123
## alternative hypothesis: true autocorrelation is greater than 0Análise:
A Arvore de Regressão Residual Standard Error de 0,5914 (melhor que o melhor modelo de Regressão linear 0,7487)
Analisando os resíduos, não vemos valores maiores do que 3 desvios padrão, nem abaixo nem acima. Olhand o gráfico de probabilidade Normal, a distribuição parece normal O teste de DW para aleatoriedade tem P-valor de 0,2%. Então podemos assumir a aleatoriedade dos resíduos
Com isso podemos concluir que a Arvore de Regressão apresenta resultados melhores do que a Regressão linear para prever a quality dos vinhos brancos, com base nos dads que temos
Para tentar melhor nossa previsão, vamos transformar a variável de resposta “quality” em uma variável discreta. A variável será “Bom_ruim”, onde 0 será para vinhos ruins (quality = 3, 4, 5) e 1 será para vinhos bons (quality = 7, 8, 9)
Criaremos um novo banco de dados chamado white2 onde só teremos os vinhos com quality diferente de 6
white1[,"Bom_ruim"] <- ifelse(white1$quality == 3, 0, ifelse(white1$quality == 4, 0, ifelse(white1$quality == 5, 0, ifelse(white1$quality == 7, 1, ifelse(white1$quality == 8, 1, ifelse(white1$quality == 9, 1, 6))))))
white2 <- subset(white1, white1$Bom_ruim != 6)
summary(white2)## quality fixedacidity volatileacidity citricacid
## Min. :3.000 Min. : 3.900 Min. :0.0800 Min. :0.000
## 1st Qu.:5.000 1st Qu.: 6.300 1st Qu.:0.2200 1st Qu.:0.260
## Median :5.000 Median : 6.800 Median :0.2800 Median :0.310
## Mean :5.779 Mean : 6.869 Mean :0.2927 Mean :0.331
## 3rd Qu.:7.000 3rd Qu.: 7.400 3rd Qu.:0.3400 3rd Qu.:0.390
## Max. :9.000 Max. :11.800 Max. :1.1000 Max. :1.000
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 22.00 1st Qu.:109.0
## Median : 5.100 Median :0.04300 Median : 34.00 Median :135.5
## Mean : 6.338 Mean :0.04619 Mean : 35.01 Mean :139.4
## 3rd Qu.: 9.800 3rd Qu.:0.05100 3rd Qu.: 46.00 3rd Qu.:169.0
## Max. :22.000 Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.790 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9918 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.40
## Median :0.9938 Median :3.170 Median :0.4700 Median :10.20
## Mean :0.9941 Mean :3.188 Mean :0.4889 Mean :10.46
## 3rd Qu.:0.9963 3rd Qu.:3.280 3rd Qu.:0.5400 3rd Qu.:11.40
## Max. :1.0024 Max. :3.820 Max. :1.0800 Max. :14.20
## fator01 Bom_ruim
## Min. :-2.32828 Min. :0.0000
## 1st Qu.:-0.79655 1st Qu.:0.0000
## Median :-0.08207 Median :0.0000
## Mean : 0.02321 Mean :0.3929
## 3rd Qu.: 0.80761 3rd Qu.:1.0000
## Max. : 2.68198 Max. :1.0000attach(white2)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white1 (pos = 5):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 8):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 9):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 12):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 13):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 14):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 16):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileaciditypar (mfrow=c(3,4))
plot (fixedacidity, Bom_ruim)
plot (volatileacidity, Bom_ruim)
plot (citricacid, Bom_ruim)
plot (residualsugar, Bom_ruim)
plot (chlorides, Bom_ruim)
plot (freesulfurdioxide, Bom_ruim)
plot (totalsulfurdioxide, Bom_ruim)
plot (density, Bom_ruim)
plot (pH, Bom_ruim)
plot (sulphates, Bom_ruim)
plot (alcohol, Bom_ruim)
attach(white2)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white2 (pos = 3):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 6):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 9):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 10):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 13):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 14):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 15):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 17):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidityModelo_RegLog0 <- glm(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, family=binomial(link="logit"))
summary(Modelo_RegLog0)##
## Call:
## glm(formula = Bom_ruim ~ fixedacidity + volatileacidity + citricacid +
## residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide +
## density + pH + sulphates + alcohol, family = binomial(link = "logit"))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.8455 -0.5814 -0.2156 0.5788 2.9851
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 887.802478 126.549694 7.015 2.29e-12 ***
## fixedacidity 0.635214 0.126503 5.021 5.13e-07 ***
## volatileacidity -9.767008 0.745034 -13.109 < 2e-16 ***
## citricacid -0.830594 0.571996 -1.452 0.146474
## residualsugar 0.443592 0.047983 9.245 < 2e-16 ***
## chlorides -8.220289 5.131638 -1.602 0.109181
## freesulfurdioxide 0.005858 0.004341 1.350 0.177157
## totalsulfurdioxide 0.002249 0.002107 1.067 0.285856
## density -917.348855 128.353867 -7.147 8.87e-13 ***
## pH 3.646380 0.591466 6.165 7.05e-10 ***
## sulphates 3.337707 0.521060 6.406 1.50e-10 ***
## alcohol 0.559339 0.157586 3.549 0.000386 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3615.4 on 2697 degrees of freedom
## Residual deviance: 2116.1 on 2686 degrees of freedom
## AIC: 2140.1
##
## Number of Fisher Scoring iterations: 6table(white2$Bom_ruim, predict(Modelo_RegLog0) > 0.5)##
## FALSE TRUE
## 0 1496 142
## 1 359 701attach(white2)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white2 (pos = 3):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 4):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 7):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 10):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 11):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 14):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 15):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 16):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 18):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidityModelo_RegLog1 <- glm(Bom_ruim ~ fixedacidity+volatileacidity+residualsugar+density+pH+sulphates+alcohol, family=binomial(link="logit"))
summary(Modelo_RegLog1)##
## Call:
## glm(formula = Bom_ruim ~ fixedacidity + volatileacidity + residualsugar +
## density + pH + sulphates + alcohol, family = binomial(link = "logit"))
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9386 -0.5828 -0.2359 0.5809 2.9527
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 899.2217 118.0834 7.615 2.63e-14 ***
## fixedacidity 0.6073 0.1210 5.017 5.24e-07 ***
## volatileacidity -9.5085 0.7074 -13.441 < 2e-16 ***
## residualsugar 0.4563 0.0455 10.030 < 2e-16 ***
## density -929.2993 119.6595 -7.766 8.09e-15 ***
## pH 3.7993 0.5766 6.589 4.44e-11 ***
## sulphates 3.4366 0.5163 6.656 2.82e-11 ***
## alcohol 0.5451 0.1543 3.532 0.000412 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3615.4 on 2697 degrees of freedom
## Residual deviance: 2128.6 on 2690 degrees of freedom
## AIC: 2144.6
##
## Number of Fisher Scoring iterations: 5ICbeta1=confint.default(Modelo_RegLog1,level=0.95)
ICbeta1## 2.5 % 97.5 %
## (Intercept) 667.7824723 1130.6609856
## fixedacidity 0.3700683 0.8445550
## volatileacidity -10.8950057 -8.1219758
## residualsugar 0.3671776 0.5455262
## density -1163.8275122 -694.7709925
## pH 2.6691027 4.9295041
## sulphates 2.4245760 4.4485818
## alcohol 0.2426526 0.8475608table(white2$Bom_ruim, predict(Modelo_RegLog1) > 0.5)##
## FALSE TRUE
## 0 1496 142
## 1 355 705OR1=exp(Modelo_RegLog1$coefficients)
ICOR1=exp(ICbeta1)
round((cbind(OR1, ICOR1)),3)## OR1 2.5 % 97.5 %
## (Intercept) Inf 1.033339e+290 Inf
## fixedacidity 1.835 1.448000e+00 2.327
## volatileacidity 0.000 0.000000e+00 0.000
## residualsugar 1.578 1.444000e+00 1.726
## density 0.000 0.000000e+00 0.000
## pH 44.670 1.442700e+01 138.311
## sulphates 31.080 1.129700e+01 85.506
## alcohol 1.725 1.275000e+00 2.334OR1 2.5 % 97.5 %
(Intercept) 0.053 0.002 1.618
idade 1.142 1.033 1.263
renda 0.042 0.002 0.726
Interpretação das razões de chance (odds ratio)
Tanto a idade quanto a renda familiar per capita estão significativamente relacionadas com a chance de autoavaliação de saúde não boa (OBS: Note que o p-valor é menor que o nível de significância de 5% e o IC para OR não inclui a unidade).
A chance do indivíduo reportar um estado de saúde não bom aumenta em 14,2% ao aumentar em 1 ano a idade.
Indivíduos com mais de 3 salários mínimos tem uma chance de reportar um estado de saúde não bom 95,8% menor do que os indivíduos que ganham no máximo 3 salários mínimos.
attach(white2)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white2 (pos = 3):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 4):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 5):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 8):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 11):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 12):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 15):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 16):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 17):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 19):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidityArvore_decisao1 <- rpart(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)
plot(Arvore_decisao1)
text(Arvore_decisao1, pretty = 0, cex = 0.6)
summary(Arvore_decisao1)## Call:
## rpart(formula = Bom_ruim ~ fixedacidity + volatileacidity + citricacid +
## residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide +
## density + pH + sulphates + alcohol)
## n= 2698
##
## CP nsplit rel error xerror xstd
## 1 0.33749371 0 1.0000000 1.0003746 0.008449526
## 2 0.07431228 1 0.6625063 0.6631321 0.019390587
## 3 0.03745862 2 0.5881940 0.5899085 0.018425056
## 4 0.01959342 3 0.5507354 0.5528783 0.018833094
## 5 0.01843187 4 0.5311420 0.5424329 0.018808386
## 6 0.01412535 5 0.5127101 0.5243125 0.018655754
## 7 0.01368686 6 0.4985848 0.5220435 0.018485267
## 8 0.01000000 7 0.4848979 0.5152687 0.018312414
##
## Variable importance
## alcohol density chlorides
## 37 24 13
## volatileacidity totalsulfurdioxide freesulfurdioxide
## 8 6 4
## residualsugar pH sulphates
## 4 2 1
##
## Node number 1: 2698 observations, complexity param=0.3374937
## mean=0.3928836, MSE=0.2385261
## left son=2 (1731 obs) right son=3 (967 obs)
## Primary splits:
## alcohol < 10.85 to the left, improve=0.33749370, (0 missing)
## density < 0.99203 to the right, improve=0.23249920, (0 missing)
## chlorides < 0.0395 to the right, improve=0.16868680, (0 missing)
## totalsulfurdioxide < 158.5 to the right, improve=0.09100253, (0 missing)
## volatileacidity < 0.2275 to the right, improve=0.05403458, (0 missing)
## Surrogate splits:
## density < 0.991935 to the right, agree=0.878, adj=0.661, (0 split)
## chlorides < 0.0385 to the right, agree=0.776, adj=0.375, (0 split)
## totalsulfurdioxide < 123.5 to the right, agree=0.702, adj=0.169, (0 split)
## residualsugar < 5.05 to the right, agree=0.658, adj=0.047, (0 split)
## sulphates < 0.335 to the right, agree=0.656, adj=0.041, (0 split)
##
## Node number 2: 1731 observations, complexity param=0.07431228
## mean=0.1808203, MSE=0.1481243
## left son=4 (1400 obs) right son=5 (331 obs)
## Primary splits:
## volatileacidity < 0.205 to the right, improve=0.18651550, (0 missing)
## alcohol < 10.11667 to the left, improve=0.05776711, (0 missing)
## pH < 3.315 to the left, improve=0.04131870, (0 missing)
## citricacid < 0.265 to the left, improve=0.03969394, (0 missing)
## chlorides < 0.0395 to the right, improve=0.02366558, (0 missing)
## Surrogate splits:
## pH < 2.915 to the right, agree=0.812, adj=0.015, (0 split)
## sulphates < 0.915 to the left, agree=0.812, adj=0.015, (0 split)
## totalsulfurdioxide < 24.5 to the right, agree=0.811, adj=0.009, (0 split)
## density < 0.990125 to the right, agree=0.810, adj=0.006, (0 split)
##
## Node number 3: 967 observations, complexity param=0.03745862
## mean=0.7724922, MSE=0.175748
## left son=6 (69 obs) right son=7 (898 obs)
## Primary splits:
## freesulfurdioxide < 11.5 to the left, improve=0.14184460, (0 missing)
## alcohol < 11.725 to the left, improve=0.10565340, (0 missing)
## fixedacidity < 7.35 to the right, improve=0.06552326, (0 missing)
## totalsulfurdioxide < 77.5 to the left, improve=0.05019448, (0 missing)
## residualsugar < 1.275 to the left, improve=0.04827922, (0 missing)
## Surrogate splits:
## totalsulfurdioxide < 55.5 to the left, agree=0.939, adj=0.145, (0 split)
##
## Node number 4: 1400 observations, complexity param=0.01412535
## mean=0.1, MSE=0.09
## left son=8 (1224 obs) right son=9 (176 obs)
## Primary splits:
## pH < 3.325 to the left, improve=0.07214506, (0 missing)
## volatileacidity < 0.2825 to the right, improve=0.06355938, (0 missing)
## alcohol < 10.25 to the left, improve=0.06301544, (0 missing)
## chlorides < 0.0445 to the right, improve=0.03032236, (0 missing)
## density < 0.993045 to the right, improve=0.02270628, (0 missing)
## Surrogate splits:
## fixedacidity < 5.45 to the right, agree=0.879, adj=0.034, (0 split)
## freesulfurdioxide < 114.25 to the left, agree=0.876, adj=0.011, (0 split)
##
## Node number 5: 331 observations, complexity param=0.01843187
## mean=0.5226586, MSE=0.2494866
## left son=10 (252 obs) right son=11 (79 obs)
## Primary splits:
## residualsugar < 12.3 to the left, improve=0.14363890, (0 missing)
## density < 0.99674 to the left, improve=0.13288490, (0 missing)
## alcohol < 9.15 to the right, improve=0.08314618, (0 missing)
## freesulfurdioxide < 24.5 to the left, improve=0.08103964, (0 missing)
## citricacid < 0.235 to the left, improve=0.05392591, (0 missing)
## Surrogate splits:
## density < 0.99674 to the left, agree=0.970, adj=0.873, (0 split)
## alcohol < 9.15 to the right, agree=0.900, adj=0.582, (0 split)
## pH < 2.965 to the right, agree=0.813, adj=0.215, (0 split)
## chlorides < 0.0555 to the left, agree=0.785, adj=0.101, (0 split)
## totalsulfurdioxide < 207 to the left, agree=0.779, adj=0.076, (0 split)
##
## Node number 6: 69 observations
## mean=0.2028986, MSE=0.1617307
##
## Node number 7: 898 observations, complexity param=0.01959342
## mean=0.8162584, MSE=0.1499807
## left son=14 (393 obs) right son=15 (505 obs)
## Primary splits:
## alcohol < 11.725 to the left, improve=0.09362169, (0 missing)
## fixedacidity < 7.35 to the right, improve=0.06222361, (0 missing)
## density < 0.991655 to the right, improve=0.04346013, (0 missing)
## residualsugar < 0.975 to the left, improve=0.04297555, (0 missing)
## chlorides < 0.0395 to the right, improve=0.04144398, (0 missing)
## Surrogate splits:
## density < 0.991115 to the right, agree=0.720, adj=0.361, (0 split)
## volatileacidity < 0.2675 to the left, agree=0.670, adj=0.247, (0 split)
## chlorides < 0.0385 to the right, agree=0.651, adj=0.204, (0 split)
## residualsugar < 1.475 to the left, agree=0.624, adj=0.140, (0 split)
## totalsulfurdioxide < 142.5 to the right, agree=0.602, adj=0.092, (0 split)
##
## Node number 8: 1224 observations
## mean=0.06944444, MSE=0.06462191
##
## Node number 9: 176 observations, complexity param=0.01368686
## mean=0.3125, MSE=0.2148438
## left son=18 (136 obs) right son=19 (40 obs)
## Primary splits:
## alcohol < 10.48333 to the left, improve=0.2329412, (0 missing)
## density < 0.9939 to the right, improve=0.2082860, (0 missing)
## volatileacidity < 0.2975 to the right, improve=0.1321515, (0 missing)
## chlorides < 0.0445 to the right, improve=0.1186099, (0 missing)
## totalsulfurdioxide < 160.5 to the right, improve=0.1121008, (0 missing)
## Surrogate splits:
## density < 0.992995 to the right, agree=0.812, adj=0.175, (0 split)
## citricacid < 0.58 to the left, agree=0.784, adj=0.050, (0 split)
## freesulfurdioxide < 7.5 to the right, agree=0.784, adj=0.050, (0 split)
##
## Node number 10: 252 observations
## mean=0.4166667, MSE=0.2430556
##
## Node number 11: 79 observations
## mean=0.8607595, MSE=0.1198526
##
## Node number 14: 393 observations
## mean=0.6819338, MSE=0.2169001
##
## Node number 15: 505 observations
## mean=0.9207921, MSE=0.07293403
##
## Node number 18: 136 observations
## mean=0.1911765, MSE=0.154628
##
## Node number 19: 40 observations
## mean=0.725, MSE=0.199375table(white2$Bom_ruim, predict(Arvore_decisao1) > 0.5)##
## FALSE TRUE
## 0 1451 187
## 1 230 830attach(white2)## The following object is masked _by_ .GlobalEnv:
##
## fator01## The following objects are masked from white2 (pos = 3):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 4):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 5):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white2 (pos = 6):
##
## alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 9):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 12):
##
## alcohol, chlorides, citricacid, density, fator01,
## fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
## sulphates, totalsulfurdioxide, volatileacidity## The following objects are masked from white1 (pos = 13):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 16):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 17):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 18):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 20):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity#Rand_F <- randomForest(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)
#Rand_Fom_forest.p <- classCenter(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, iris.rf$prox)
#plot(iris[,3], iris[,4], pch=21, xlab=names(iris)[3], ylab=names(iris)[4],
#bg=c("red", "blue", "green")[as.numeric(factor(iris$Species))],
#main="Iris Data with Prototypes")
#points(iris.p[,3], iris.p[,4], pch=21, cex=2, bg=c("red", "blue", "green"))